Magnetic circuits

Electromagnetic Principles and Magnetic Circuits

1. ELECTROMAGNETIC PRINCIPLES
AND MAGNETIC CIRCUITS
Dr. SELVARASU RANGANATHAN
Professor
School of Electrical Engineering and Computing
AdamaScience and Technology University
Adma, Ethiopia

4. MAGNETIC FIELDS
Magnet:
A substance that attract the iron pieces and pieces of
some other metal is called magnet.
A magnet can be classified into a permanent and temporary
magnet.
(i) Permanent magnet
This is made up of Cobalt, Steel or Tungsten steel. It is used in moving coil
instruments, energy meters, loud speakers and microphones etc.,.
(ii) Temporary Magnet.
It is also called an electromagnet. The material used here is soft iron or Silicon
steel. A soft iron piece with a coil acts as a magnet as long as current flows through the
coil. It is used in electrical machines such as motor and generator.

5. MAGNETIC FIELDS
Magnetic lines of Force:
Theimaginarymagneticlineswhichtravelfromnorthpole
tosouthpoleoutsidethemagnet,andsouthpoletonorthpole,
insidethemagnetarecalledmagneticlinesofforce.
Magnetic Field
The region around which the magnetic lines of force acts is called
magnetic field.

6. MAGNETIC FIELDS
Properties of Magnetic lines of Force:
•Magneticlinesofforcearedirectedfromnorthtosouthoutsidea
magnet.Thedirectionisdeterminedbythenorthpoleofasmallmagnet
heldinthefield.
•Magneticlinesofforcearecontinuous.
•Magneticlinesofforceenterorleaveamagneticsurfaceatrightangles.
•Magneticlinesofforcecannotcrosseachother.
•Magneticlinesofforceinthesamedirectiontendtorepeleachother.
•Magneticlinesofforcetendtobeasshortaspossible.
•Magneticlinesofforceoccupythree-dimensionalspaceextending
(theoretically)toinfinity.

7. MAGNETIC FIELDS
Electromagnetism:
Amagneticfieldisalwaysassociatedwithacurrent-carryingconductor,
asillustratedinFigure.Exploringthemagneticfieldbymeansofacompass,we
observethefollowing:
Themagneticfieldisstrongestperpendiculartothecurrentdirection.

8. MAGNETIC FIELDS
Ampere's right-hand rule :
Ifwegrasptheconductorwithourrighthand,thethumbpointingin
thedirectionofthecurrent,ourfingerswillpointinthesamedirectionasthe
northpoleofthecompass.Thismethodofdeterminingthedirectionsof
currentflowinaconductorandthesurroundinglinesofforceiscalledAm-
pere'sright-handruleasillustratedinFigure.

9. MAGNETIC FIELDS
Wecandeterminethedirectionofthemagneticfieldinacylindrical
coilofmanyturnsofinsulatedwirebyusingourrighthand.Ifwegraspthecoil
withourrighthandwiththefingerspointinginthedirectionofthecurrent,the
thumbwillpointinthedirectionofthenorthpole.Thismethodofdetermining
directionsofcurrentflowinacoilandmagneticfieldsofforceisanotherform
ofAmpere'sright-handrule.
Magnetic field direction of solenoid by right hand rule

10. ELECTROMAGNETIC RELATIONSHIPS
Magnetic Flux (Φ)
Thetotalnumberoflinesofforceinthemagneticfieldiscalled
magneticflux.Itisdenotedby‘Φ’,anditsunitisWeber.
Magnetic Flux Density (B)
Themagneticfluxpassingthroughunitcrosssectioniscalledflux
density.Itisdenotedby‘B’.
If‘Φ’ismagneticfluxinWebers
BisfluxdensityinWb/m2.
thenB=Φ/AWb/m
2
Magneto-Motive Force (MMF)
Itisthedrivingforcerequiredtodrivethemagneticfluxthrougha
magneticcircuit.
TheproductNIiscalledmagneto-motiveforce.ItsunitisAmpereturns.
MMF=NI(AT)

11. ELECTROMAGNETIC RELATIONSHIPS
Reluctance (S)
Itisthepropertyofmagneticmaterialbywhichitopposesthe
establishmentofmagneticflux.Itisdefinedastheratioofmagneto-motive
forcetotheflux.ItisdenotedbySanditsunitisampereturns/Wb.
Reluctance, S =mmf/flux=NI/Φ(AT/Wb)
Permeance
It is the reciprocal of reluctance and is a measure of the case with
which flux can pass through the material. Its unit is Wb/AT.
Permeance= 1/S (Wb/AT)

12. ELECTROMAGNETIC RELATIONSHIPS
Magnetic Field Strength (H)
It is given by the force experienced by unit north pole
placed at that point. It is denoted by ‘H’.
If ‘Φ’ is the flux in webers
‘F’ is the force in Newton (Nw)
H is the field strength in Nw/Wb.
thenH = F/Φ(Nw/Wb)
H is also given by H =B/µ
oµ
r(Nw/Wb)

13. ELECTROMAGNETIC RELATIONSHIPS
Permeability
The magnetic conductivity of iron as compared to that of air is called
permeability.
The absolute permeability ‘µ’ of a medium is given by, µ=B/H
where B =flux density in Wb/m2
H = magnetic field strength in Nw/Wb
µis also given by the equation, µ=µ
oµ
r
Where µ
o= 4¶ x 10
-7
H/Mand µ
r= Relative permeability
The relative permeability µ
rof a medium is given by µ
r= B/B
0
where B = flux density in the medium under consideration in Wb/m
2
B
0= flux density in vacuum.
The value of µ
r=1 for air, free space or vacuum.

14. MAGNETIC CIRCUIT
Analysis of Magnetic Circuit
Amagneticcircuitisdefinedas,theclosedpathtracedby
themagneticlinesofforce.
The magnetic circuit can be sub divided into,
(i) Simple magnetic circuit
(ii) Composite magnetic circuit
(iii) Parallel magnetic circuit

15. MAGNETIC CIRCUITS
(i) Simple Magnetic Circuit
Itconsistsofaclosedironringwoundwithamagnetisingcoilas
showninfig.Themagneticfluxisproducedbythecoil.Thusthecoilactsasa
sourceofmmfandthereluctancefortheestablishmentofmagneticfluxis
offeredbytheironring.
The torroidalring with a coil of ‘N’ turns.
Let I = current through the coil
Φ = flux in the iron ring (Wb)
A = Area of cross section of the ring (m
2
).
l = length of the magnetic path in metres
µ
o= 4¶ x 10
-7
H/Mand µ
r= Relative permeability of the ring.

16. MAGNETIC CIRCUITS
(i) Simple Magnetic Circuit Contd…

17. MAGNETIC CIRCUITS
(ii) Composite Magnetic Circuit
Practicallythemagneticcircuitsareformedbymorethanonematerial,
withdifferentpermeability.Suchmaterialscanhavevariouslengthandcross
sectionalarea.Thiscircuitiscalledascompositecircuit.Whenthosematerials
areconnectedoneaftertheothertoformamagneticcircuitiscalledtobe
seriesmagneticcircuit.

18. MAGNETIC CIRCUITS
(ii) Composite Magnetic Circuit Contd..

19. MAGNETIC CIRCUITS
(ii) Composite Magnetic Circuit Contd..

20. MAGNETIC CIRCUITS
(iiI) Parallel Magnetic Circuits
A magnetic circuit is said to be parallel connected if it has more than
one closed path for flux.
At point B, flux have two paths.
(i) flux Φ
2passes through the path BE
(ii) flux Φ
3passes through the path BCFE.

21. MAGNETIC CIRCUITS
(iiI) Parallel Magnetic Circuits contd…

22. MAGNETIC CIRCUITS
Magnetic Leakage
Thefluxthatfollowsanundesiredpathiscalledtheleakageflux.To
utilizethemagneticfluxestablishedbythemagneticmaterial,weprovideanair
gap.Thefluxintheairgapiscalledusefulflux.
Thefluxwhichdoesnotpassthroughtheairgap,cannotbeutilized
andhenceitisconsideredasleakagefluxwhichcanbedeterminedbya
compass.Though,thisleakagefluxdoesnotaffecttheefficiencyofthe
electricalmachinedirectly,itdoesincreasetheweightandcostandhenceitis
undesirable.Itcannotbetotallyavoidedbutcanbeminimisedbywindingthe
excitingcoilsofcloselyaspossibletotheairgap.

23. Comparison of Electric and Magnetic
Circuit
S.NoMagnetic Circuit Electric Circuit
1The path traced by magnetic flux is
defined as magnetic circuit.
Path traced by the current is called as
electric circuit.
2MMF is the driving force in the
magnetic circuit (Unit is Ampere turns)
Emfis the driving force in an electric
circuit. (Unit is volts)
3There will be the presence of flux,
(Wb)
There will be the presence of current,
I (A)
4The magnetic lines will decide the fluxThe electrons will decide the current.
(i) Similarities

24. Comparison of Electric and Magnetic
Circuit
(ii) Disimilarities

25. ELECTROMAGNETIC INDUCTION
We have seen the magnetic effects of an electric current. Then it was
Michael Faraday who made attempts, to get emffrom magnetic flux. This is
called to be electromagnetic induction.
Law of Electromagnetic Induction
(i) Faraday’s law
Wheneverthemagneticfluxlinkingaconductorchanges,anemfis
alwaysinducedinit.Themagnitudeofinducedemfisproportionaltotherate
ofchangeoffluxlinkages.
e=NdΦ/dt
Wheree=inducedemfinV
N=Numberofturns
dΦ/dt=Rateofchangeofflux.

26. ELECTROMAGNETIC INDUCTION
(iI) Lez’sLaw
This law states that any induced emfwill circulate a current in such a
direction so as to oppose the cause producing it.
e= -N dΦ/dt
Wheree=inducedemfinV
N=Numberofturns
dΦ/dt=Rateofchangeofflux.

27. NATURE OF INDUCED EMF
Wecangetinducedemffromaconductor,wheneverthereischangein
flux,withthatconductor.
Wecanobtainthisfromtwomethods.So,theemfisclassifiedas,
(i)Dynamicallyinducedemfand
(ii)Staticallyinducedemf.
(i) Dynamically Induced emf
When the induced emfis from the mechanical movement of coil with
respect to flux, (or) movement of magnet with respect to stationary coil, then it
is called Dynamically induced
emf.
Eg: DC generator, AC generator.
The induced emfwill be given by,
e = Blvsin Ɵ (V).
Direction of dynamically induced emfis found by Fleming’s Right Hand Rule.

28. NATURE OF INDUCED EMF
Fleming’s Right Hand Rule
Stretchtheforefinger,middlefingerandthumbofright
handmutuallyperpendiculartoeachother.Ifforefinger
representsthedirectionofmagneticfield,thumbrepresentsthe
directionofmotionofconductorthenthemiddlefingerwill
representthedirectionofinducedemf.

29. NATURE OF INDUCED EMF
(ii)Staticallyinducedemf.
Theinducedemfinacoilwithoutanymechanical
movementofcoil(or)magnetiscalledstationaryinducedemf(or)
staticallyinducedemf.
Thisisachievedbychangingthefluxassociatedwithacoil,
byincreasing(or)decreasingthecurrentthroughitrapidly.
Staticallyinducedemfisfurtherclassifiedas,
(a)Selfinducedemf
(b)Mutuallyinducedemf

30. NATURE OF INDUCED EMF
(a)Selfinducedemf
In the set up shown in Fig. the coil is carringa current of I, amps. Due
to this current, flux will be established.
Whenthiscurrentisvariedbyvaryingthevalueof
resistance,thefluxlinkingthecoilalsochanges.
So,anemfwillbeinduced.Thisiscalledself-
inducedemf.
Simply,theemfinducedinacoilduetothe
changeofitsownfluxlinkedwithitiscalledself
inducedemf.
Theselfinducedemfwillbeinducedtill
thecurrentinthecoilischangingandalsoits
directioncanbeobtainedfromLenz’slaw.

31. NATURE OF INDUCED EMF
(ii) Mutually induced emf
Consider two coils (Say A and B) which are kept near by.
ThechangeinfluxincoilAwillchangethefluxlinkingwithcoilB.Due
tothisanemfwillbeinducedincoilB.Thisinducedemfiscalledasmutually
inducedemf.
Simply,theemfinducedinacircuitduetothechangeinthenearby
circuitiscalledasmutuallyinducedemf.
InFig.thefluxincoilAislinkingthecoilB.
So,whenthecurrentflowing
throughcoilA(I
1)isvaried,thenΦ
1willbe
varied,whichinturnchangesΦ
12,theflux
linkingcoilAandcoilB.Duetothis
variationinthefluxlinkage,emfwillbe
inducedincoilBandthegalvanometer
pointerwilldeflectinonedirection.The
currentI
1isvariedbyvaryingtheresistance
R,inthecoilAcircuit.

32. HYSTERESIS LOOP
When we plot the variation in the magnetic parameters with the
change in current, then the result in curve or loop is called as hysteresis curve or
hysteresis loop.
As we know that alternating voltages increases and decreases with respect to
time periodically. In the positive half cycle it magnetisesthe magnetic circuit
and in the negative half cycle it demagnetises. It is also called as AC operation of
magnetic circuits.

33. CORE LOSSESS
CoreLossessareclassifiedas
(i)Hysteresisloss
(ii)EddyCurrentloss
(i) Hysteresis Loss
Whenamagneticmaterialissubjectedtoacycleofmagnetisationand
demagnetisation,someoftheenergylosswilloccurduetomolecularfriction.
Energyisthusexpandedinthematerialinovercomingthisopposition.Thisloss
isintheformofheatandiscalledhysteresisloss.Itissocalledbecauseit
resultsduetothehysteresiseffectinamagneticmaterial.Thiseffect-resultsin
theriseoftemperatureofthemachine.
Hysteresis loss = ηBmax
1.6fv (J/S) or Watts.
where,
η =Steinmentzhysteresis co-efficient
f = frequency of reversal of magnetisation
v = volume of magnetic material

34. CORE LOSSESS
(ii) Eddy Current Loss
Whenamagneticmaterialissubjectedtoachangingmagneticfield,in
additiontothehysteresisloss,anotherlossthatoccursinthematerialisthe
eddycurrentloss.Thechangingfluxinducesemfinthematerial.Duetothis
emf,thecurrentwillflowwhichdoesnotdousefulwork.Itisknownaseddy
currents.Thislossalsoresultsinriseinthetemperatureofthematerial.
Eddy current loss depends on the various factors which are,
(i) Nature of material.
(ii) Maximum flux density.
(iii) Frequency
(iv) Thickness of laminations used to construct the core
(v) Volume of magnetic material
Eddy current loss = K
e(B
max)
2
f
2
t
2
v (Watts)
Eddy current loss can be minimisedby laminating the core.